Monad Transformer - SML

The basic idea is we want to combine monads together. Towards that end, we have a SML Functor which will "eat in" a monad, and produce a monad.

We have to implement an individual monad transformer as an individual functor. For example,

functor StateT(type state
               structure M : MONAD) : MONAD =
struct
  type state = state;
  (* Type constructor *)
  type 'a t = (state -> 'a * state) M.t;

  fun return x = fn s => M.return (x,s);

  fun bind m f = fn s => M.bind (m s) (fn (x, s') => f x s');

  fun lift m = fn s => M.bind m (fn x => M.return (x,s));

  (* etc. *)
end;

• Sheng Liang, Paul Hudak, Mark Jones,
  "Monad transformers and modular interpreters".
  In POPL '95: Proceedings of the 22nd ACM SIGPLAN-SIGACT symposium on Principles of programming languages, January 1995, pp.333–343 https://doi.org/10.1145/199448.199528
• Mark P Jones,
  "Functional Programming with Overloading and Higher-Order Polymorphism".
  Eprint, 1995, 40 pages.
• Martin Grabmuller,
  "Monad Transformers Step by Step".
  Citeseer 2006 draft.